More than three-quarters of universities in England are to have their budgets cut for this September – some by nearly 14%, triggering warnings of larger class sizes, further job cuts and a deterioration in the quality of courses.

The universities of Oxford and Cambridge are among 99 institutions that will be forced to cope with reduced state funding for the next academic year, as colleges prepare for the harshest financial climate in more than a decade.

Universities have not witnessed cuts on this scale since 1997, the government agency in charge of distributing public money to them – the Higher Education Funding Council for England (Hefce) – admitted yesterday.

London Business School has had its state funds slashed by 13.9% in real terms, while the London School of Economics and Political Science and the highly regarded Courtauld Institute of Art in London will have to cope with 8.3% and 12.9% cuts respectively.

Oxford and Cambridge universities will have their overall budgets reduced by 1% and 1.9% respectively, although this is mainly because a grant of £40m to preserve historic buildings has been withdrawn. Other leading universities, such as Birmingham, Bristol, Durham, Leeds and Manchester will have to endure real-term cuts of between 1.3% and 3.2%.

In total, Hefce will hand out £7.36bn in state funds to 130 universities and colleges for their teaching, research and building projects, a 3.6% real-term drop on the sum awarded for this academic year.

Wendy Piatt, director general of the Russell Group of 20 leading research-intensive universities, said the cuts would pose "real challenges" for institutions and came as competitors in Europe, Asia and the US were "pouring more resources into higher education as a strategy for coming out of recession".

Sally Hunt, the general secretary of the academics' trade union, the University and College Union, said: "Anyone who thinks this won't massively impact on the quality of education in this country is living in a dream world."

Alan Langlands, Hefce's chief executive, said the funding reductions would not undermine the quality of higher education: "I don't think anyone is prepared to watch the gains of recent years in higher education disappear. These are very modest reductions. I think it is quite likely that universities will be able to cope with these without undermining in any way the student experience."

David Lammy, the higher education minister, said: "These changes come after years of sustained investment. Higher education funding is up by 25% in real terms since 1997. Like everyone in the current financial climate, institutions have to do their fair share of belt-tightening."

While leading universities have suffered overall budget cuts, their research grants have stayed the same or risen. Oxford's research grant will grow by 6% to £126m and Cambridge's will rise by 3.7% to £118m. The country's two oldest universities will receive 15% of all funds for research.

Hefce said it would now concentrate the £1.6bn it allocates for research alone to fewer universities, rather than spread it across 130 institutions. Just 10 universities will be given 49% of all research money.

Last month, Hefce announced how much less all universities would receive compared with last year, but did not reveal each university's allocation. The funding council has cut teaching budgets by £215m – 1.6% less in real terms than last year and the first time in a decade that teaching has been cut.

The amount universities are given for encouraging those from the poorest backgrounds to apply has also gone down by 0.75% to £144m. Grants for capital projects, such as new buildings, have been cut by 14.9% in cash terms to £562m. This is the equivalent of a £142m cut.

The cuts come ahead of an independent review on whether students should pay higher tuition fees. The review, led by the former BP chief executive, Lord Browne, is due after the general election and could see fees rise from £3,225 a year to more than £5,000. However, it is likely that universities would only be allowed to charge higher fees if they could provide financial support to students who could not afford the fees.

The cuts also come as record numbers apply for university. Seven students are expected to compete for each place awarded this summer. The Conservatives have estimated that 275,000 students will miss out on a place. Ucas applications have grown by 23% – or 106,389 – so far this year, but the number of places has been reduced by 6,000. Mary Curnock Cook, the head of Ucas, has said would-be university students will have to "reappraise their aspirations".Hefce said it needed to cap student numbers to 380,000 first-year undergraduates – 6,000 fewer than last year. Unless a cap was in place, the public cost to fund bursaries for students who could not otherwise afford university would spiral out of control.

Million+, a lobby group which represents some of the ex-polytechnics, said the cut in capital funding would cause "long-term problems" for some of the newer universities, while the drive to concentrate research funding would "undermine innovation in those universities which have historically received less money but have more than proved their worth in promoting world-leading research".